a circular disc of radious' s= 3cm has been
rimoved from a large disc of Radious R=10cm.
The centre of the hole so made it at
a=5cm. distance from the centre of original
disc. if the mass of the remaining disc is 182
gm. then calculate its m.I about an axis passing through
two centres . what is its M.I. about an axis
Passing thorough 'o'
and perpendicular to its plane
Answers
Answer:
B
Step-by-step explanation:
Solution :
In Fig.
is the centre of circular disc of radius
and mass
is centre of disc of radius
, which is removed. If
is mass per unit area of disc, then
<br> Mass of disc removed,
<br> Mass of remaining disc,
<br>
<br> Let centre of mass of remaining disc be at
where
<br> As
<br>
<br>
Step-by-step explanation:
11th
Physics
Systems of Particles and Rotational Motion
Centre of Mass
A circular disc of radius R...
Physics
A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is at a distance of αR from the centre of the bigger disc. The value of α is _______.
Medium
Answer
Let the mass per unit area of the disc be σ
radius is 2R
then mass of the original disc is M=π(2R)
2
σ=4πR
2
σ
Radius of the disc cut is R
them mass of the smaller disc M
′
=πR
2
σ=
4
M
Let O and O
′
be the centers of the original disc and the disc cut off from the original.
It is given that OO
′
=R
After the smaller disc has been cut from the original, the remaining portion is considered to be system of two masses. The two masses are M and −M
′
=−
4
M
The negative sign indicates the mass has been removed from the original disc.
Let x be the distance through which the center of mass of the remaining portion shifts from point O
the relation between the center of masses of two masses as
x=
m
1
+m
2
m
1
r
1
+m
2
r
2
x=
M−M
′
M×0−M
′
×R
x=
M−
4
M
M×0−
4
M
×R
x=
4
3M
−
4
MR
=
3
−R
therefore α=
3
1